Lived there for 37 years and deer hunted since I was 16. Public land is tough to find but if you put your time in you can find some good places to hunt.
The great lakes get pounded on during all the hunting seasons and small bucks are the norm. The Mississippi is awesome country with some big river bottom bucks but can be tough to get to even with a boat unless you have ample time to do some scouting. If you are looking at the Mississippi then I would suggest the NE corner (Allamekee County) of the state. Awesome number of deer and good numbers of big bucks too. The SE corner (Keokuk) is full of deer as well but I have not had the opportunity to hunt that protion of the state. A great resource for public land is "The Sportsmans Atlas" ( 1-800-568-8334), it'll cost ya about $22 but well worth it. You can google it too. Dave Adams is the creator and has done an incredible job with this map!! If ya order one tell them Big Al and Cookie say Hi!! Might get ya a discount too.
Now if it were my tag and I was heading in without having pvt land to hunt I would head to the Loes Hills area south of Sioux City or along the Missouri River bottom. The Loes Hills is rugged county, by Iowa standards, and kicks out some of the biggest whitestail in the state and has by far the largest number of big tails too. Only thing being is this terrain is tough to hunt, but those that do there home work and put in the time and know what they are doing walk away well rewarded. I have seen first hand the class of bucks come from this area. Oh and not to forget the area is lightly hunted too. Check out the Missouri Valley, Iowa area. There are a few outfitters that run around this area too and they could be off some assistance.
Not far south of the Sloan, Iowa is a pretty good string of public land to that lays along the Missouri River. This area gets more hunting pressure that the Loes hills but kicks out some great buck too.
I have also found in the center portion of the state, Corning Iowa area that it isn't all that tough to find good pvt land to hunt. They have so many deer running around these parts that quite a few are more than willing to open their land up to you and typically for no fee. What we did in this case was get a plat book of the areas local land owners and started knocking on doors and before to long we had more land than what we new what to do with.
Good luck and tell the folks back in Iowa Tailchasers says hi!! Let me know if you have any other questions...